Vinal is a no go for common sense reasons but as far as ceramic and stone make sure it is also heat resistant or able to handle some heat but most definitely you can. Make sure you use a sealant that is non toxic to seal the grout and tile tops a couple coats should be fine possibly reseal about once a year more often if you have heavy counter usage. Good luck, have fun and post a picture here when you are finished with your project, it will be good to see a finished project that was finished and usable too!

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As an added thought if you need space next to the stove for hot pans etc, consider having a cutting board made at a local cabinet makers shop to the thickness of the tiles or a nylon one you can purchase at your local kitchen store etc to be level at the top with the tiles, this will give you a safety zone for hot pans with no fear of breaking a tile. Possibly have it so you are able to remove it for cleaning and sanitation, pop it out, clean in and under, pop it in!

I had ceramic tile on my kitchen counter is my last house. I did not care for it. The grout is a pain to clean, same as floor grout. And crumbs get caught in the grout, not as easy to just wipe clean as with formica or corian